Train Question: Max Acceleration 0.756m/s^2

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In summary, to determine the maximum rate at which the speed of a passenger train traveling at 25m/s around a circular curve of 1000m radius can be decreased without exceeding a total acceleration of g/10, the formula for radial acceleration (Arad = V^2/R) can be used. From this, the magnitude of the unknown component of acceleration can be solved for using the equation Sqrt(.625^2 + A^2) = .981. The resulting maximum rate of speed decrease is 0.756 m/s^2. Knowing how to add vectors and using the centripetal acceleration equation are helpful in solving this problem.
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madahmad1
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1.A passenger train is traveling at 25m/s around a circular curve of 1000 m radius. if the maximum total acceleration is not to exceed g/10, determine the maximum rate at which the speed may be decreased. Take g = 9.81 m/s^2.

Answer is 0.756 m/s^2, but what steps do i take to find the answer?
 
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  • #2
centripetal acceleration equation and knowing how to add vectors is a good start
 
  • #3
Wow I actually got this one :)

You are given the velocity V of the Train (25m/s) and the radius R of the circle (1000m)
From this you can use the formula Radial Acceleration Arad = V^2 / R to get the Radial Acceleration (That is the acceleration toward the center of the circle to make the velocity change direction)

Plug those in and you will get Arad = .625

Now you know that you want the magnitude of total acceleration to be g/10 or .981, and you know one of the components of acceleration, Arad to be .625. Since you know both of these you can solve for the unknown component of accleration which will be tangent to the circle

Sqrt( .625^2 + A^2 ) = .981

Do the algebra and you will get the answer to be .756 m/s^2
hopefully that makes sense.
 

What is the meaning of "Max Acceleration 0.756m/s^2"?

The term "Max Acceleration" refers to the maximum rate at which the speed of an object changes. In this case, the maximum acceleration is 0.756 meters per second squared, which means that the speed of the train will increase by 0.756 meters per second every second.

How is max acceleration measured?

Max acceleration is typically measured using an accelerometer, which is a device that measures changes in velocity. The device records the acceleration in meters per second squared (m/s^2).

Why is max acceleration important for trains?

Max acceleration is important for trains because it affects the overall speed and performance of the train. A higher max acceleration means the train can reach higher speeds in a shorter amount of time, while a lower max acceleration may result in slower speeds and longer travel times.

How does max acceleration impact passenger comfort?

Max acceleration can impact passenger comfort by causing sudden jerks or jolts if the train accelerates too quickly. It is important for trains to have a smooth acceleration to ensure a comfortable ride for passengers.

Can max acceleration be increased?

Yes, max acceleration can be increased by using more powerful engines or by reducing the overall weight of the train. However, safety regulations must also be considered when determining the max acceleration of a train.

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